108y^2-56y-32=0

Solution for 108y^2-56y-32=0 equation:

108y^2-56y-32=0

a = 108; b = -56; c = -32;
Δ = b2-4ac
Δ = -562-4·108·(-32)
Δ = 16960
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{16960}=\sqrt{64*265}=\sqrt{64}*\sqrt{265}=8\sqrt{265}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-8\sqrt{265}}{2*108}=\frac{56-8\sqrt{265}}{216}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+8\sqrt{265}}{2*108}=\frac{56+8\sqrt{265}}{216}
$